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On the zero-multiplicity of the k-generalized Fibonacci sequence
Journal of Difference Equations and Applications ( IF 1.1 ) Pub Date : 2020-12-17 Jonathan García, Carlos A. Gómez, Florian Luca
中文翻译:
关于k广义斐波那契数列的零重数
更新日期:2020-12-17
Journal of Difference Equations and Applications ( IF 1.1 ) Pub Date : 2020-12-17 Jonathan García, Carlos A. Gómez, Florian Luca
The k-generalized Fibonacci sequence is the linear recurrent sequence of order k, whose first k terms are and each term afterwards is the sum of the preceding k terms. In this paper, we extend to negative indices and give an upper bound on the absolute value of its largest zero in terms of k. In particular, we find that the zero-multiplicity of the k-generalized Fibonacci sequence is exactly for all . We prove that the zero multiplicity of the k-generalized Fibonacci sequence is at least for all .
中文翻译:
关于k广义斐波那契数列的零重数
所述ķ -generalized斐波纳契数列是阶k的线性递归序列,其前k个项是之后的每个项是前k个项的总和。在本文中,我们扩展到负指数,并以k为单位给出其最大零的绝对值的上限。特别是,我们发现k广义斐波那契数列的零重数正好是 对全部 。我们证明了k广义斐波那契数列的零多重性至少为 对全部 。